Maximum Likelihood Estimation of the Multivariate Normal Mixture Model

The Hessian of the multivariate normal mixture model is derived, and estimators of the information matrix are obtained, thus enabling consistent estimation of all parameters and their precisions. The usefulness of the new theory is illustrated with two examples and some simulation experiments. The newly proposed estimators appear to be superior to the existing ones.Mixture model; Maximum likelihood; Information matrix

"On the estimation of a large sparse Bayesian system: the Snaer program"

The Snaer program calculates the posterior mean and variance of variables on some of which we have data (with precisions), on some we have prior information (with precisions), and on some prior indicator ratios (with precisions) are available. The variables must satisfy anumber of exact restrictions. The system is both large and sparse. Two aspects of the sta-tistical and computational development are a practical procedure to solve a linear integer system, and a stable linearization routine for ratios. We test our numerical method to solve large sparse linear least-squares estimation problems, and find that it performs well, even when the n ~k design matrix is large(nk equivalent 2^27.5).

"On some definitions in matrix algebra"

Many definitions in matrix algebra are not standardized. This notediscusses some of thepitfalls associated with undesirable orwrong definitions, anddealswith central conceptslikesymmetry, orthogonality, square root, Hermitian and quadratic forms, and matrix derivatives.

Posterior moments and quantiles for the normal location model with Laplace prior

We derive explicit expressions for arbitrary moments and quantiles of the posterior distribution of the location parameter eta in the normal location model with Laplace prior, and use the results to approximate the posterior distribution of sums of independent copies of eta

Climate change, economic growth, and health

This paper studies the interplay between climate, health, and the economy in a stylized world with four heterogeneous regions, labeled 'West' (cold and rich), 'China' (cold and poor), 'India' (warm and poor), and 'Africa' (warm and very poor). We introduce health impacts into a simple integrated assessment model where both the local cooling effect of aerosols as well as the global warming effect of CO2 are endogenous, and investigate how those factors affect the equilibrium path. We show how some of the important aspects of the equilibrium, including emission abatement rates, health costs, and economic growth, depend on the economic and geographical characteristics of each region.

A general bound for the limiting distribution of Breitung's statistic

Author's draft, December 21, 2007We consider the Breitung (2002, Journal of Econometrics 108, 343–363) statistic ξn, which provides a nonparametric test of the I(1) hypothesis. If ξ denotes the limit in distribution of ξn as n → ∞, we prove (Theorem 1) that 0 ≤ ξ ≤ 1/π2, a result that holds under any assumption on the underlying random variables. The result is a special case of a more general result (Theorem 3), which we prove using the so-called cotangent method associated with Cauchy's residue theorem

Practical use of sensitivity in econometrics with an illustration to forecast combinations

Sensitivity analysis is important for its own sake and also in combination with diagnostic testing. We consider the question how to use sensitivity statistics in practice, in particular how to judge whether sensitivity is large or small. For this purpose we distinguish between absolute and relative sensitivity and highlight the context-dependent nature of any sensitivity analysis. Relative sensitivity is then applied in the context of forecast combination and sensitivity-based weights are introduced. All concepts are illustrated through the European yield curve. In this context it is natural to look at sensitivity to autocorrelation and normality assumptions. Different forecasting models are combined with equal, fit-based and sensitivity-based weights, and compared with the multivariate and random walk benchmarks. We show that the fit-based weights and the sensitivity-based weights are complementary. For long-term maturities the sensitivity-based weights perform better than other weights

Some equivalences in linear estimation (in Russian)

Under normality, the Bayesian estimation problem, the best linear unbiased estimation problem, and the restricted least-squares problem are all equivalent. As a result we need not compute pseudo-inverses and other complicated functions, which will be impossible for large sparse systems. Instead, by reorganizing the inputs, we can rewrite the system as a new but equivalent system which can be solved by ordinary least-squares methods.Linear Bayes estimation, best linear unbiased, least squares, sparse problems, large-scale optimization

The efficiency of top agents: An analysis through service strategy in tennis

We consider the question whether top tennis players in a top tournament (Wimbledon) employ an optimal (efficient) service strategy. While we show that top players do not, in general, follow an optimal strategy, our principal result is that the estimated inefficiencies are not large: the inefficiency regarding winning a point on service is on average 1.1% for men and 2.0% for women, implying that–by adopting an efficient service strategy–players can (on average) increase the probability of winning a match by 2.4%-points for men and 3.2%-points for women. While the inefficiencies may seem small, the financial consequences for the efficient player at Wimbledon can be substantial: the expected paycheck could rise by 18.7% for men and even by 32.8% for women. We use these findings to shed some light on the question of whether economic agents are successful optimizers

Climate Change, Economic Growth, and Health

This paper studies the interplay between climate, health, and the economy in a stylized world with four heterogeneous regions, labeled ‘West’ (cold and rich), ‘China’ (cold and poor), ‘India’ (warm and poor), and ‘Africa’ (warm and very poor). We introduce health impacts into a simple integrated assessment model where both the local cooling effect of aerosols as well as the global warming effect of CO2 are endogenous, and investigate how those factors affect the equilibrium path. We show how some of the important aspects of the equilibrium, including emission abatement rates, health costs, and economic growth, depend on the economic and geographical characteristics of each region.